A $4$ cylinder, $4$ stroke diesel engine develops $83\mathrm{.}5$ kW at $1800$ rpm with specific fuel consumption of $0\mathrm{.}231$ kg$/$kWh$,$ and air$/$fuel ration of $23$:$1.$ The analysis of fuel is $87\%$ carbon and $13\%$ hydrogen, and the calorific value of the fuel is $43\mathrm{.}5$ MJ$/$kg$.$ The jacket water cooling flows at $0\mathrm{.}246$ kg$/$s and its temperature rise is $50$ K$.$ The exhaust temperature is $3160$C$.$ Draw up an energy balance for the engine. Take R$=0\mathrm{.}302$ kJ$/$kg and Cp is $1\mathrm{.}09$ kJ$/$kg K for the dry exhaust gases and Cp is $1\mathrm{.}86$ kJ$/$kgK for super heated steam. The temperature in the test house is $17\mathrm{.}80$C$,$ and the exhaust gas pressure is $1\mathrm{.}013$ bar.